# Mathematical model
## MicroSim spec
- **Recommended sim type:** state-machine
- **Microsimmability score:** 34/100
- **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below.
### Parameters (tunable controls)
- `Input symbol` (event fed to the machine)
- `States` (number of states in the machine)
- `Step speed` (transition animation rate)
### What animates
A finite-state machine highlights its active state and fires transitions as input symbols arrive, accepting or rejecting the [[Sequence|sequence]].
### Learning objective
Trace how states and transitions process an input sequence.
## Links (Wikipedia order)
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`Abstract_and_concrete` · [[Agent-based_model]] · `All_models_are_wrong` · `Applied_mathematics` · `Bayesian_statistics` · [[Black_box]] · `Boolean_data_type` · `Broyden's_method` · `Business` · `Cambridge_University_Press` · [[Catastrophe_theory]] · `Causality` · [[Chaos_theory]] · `Chronometry` · `Classical_mechanics` · `Clifford_Truesdell` · `Cliodynamics` · `Computational_model` · [[Computer_science]] · `Computer_simulation` · `Conceptual_model` · `Constant_(mathematics)` · `Constitutive_equation` · `Constraint_(mathematics)` · `Cross-validation_(statistics)` · `Curve_fitting` · `Dead_reckoning` · [[Decision_theory]] · `Deterministic_finite_automaton` · `Deterministic_system` · [[Differential_equation]] · `Differential_operator` · `Economic_model` · `Economist` · [[Engineering]] · `Euclidean_geometry` · [[Evolution]] · `Exogeny` · [[Experience]] · `Exponential_decay` · `Extrapolation` · `Function_(mathematics)` · `Fungus` · [[Game_theory]] · `Gary_Chartrand` · `General_equilibrium_theory` · `General_relativity` · [[Geometry]] · `Goal` · `Governing_equation` · [[Grey_box_model]] · `Initial_condition` · `Input–output_model` · `Integer` · `International_Mathematical_Modeling_Challenge` · `Interpolation` · [[Isaac_Newton]] · `Jet_engine` · `Kinematics` · `Kleene_star` · `Language_of_mathematics` · [[Linear_algebra]] · `Linear_equation` · `Linear_model` · `Linearization` · `Logistic_function` · `Loss_function` · [[Machine_learning]] · `Malthusian_growth_model` · `Map_projection` · `Mary_S._Morgan` · `Mathematical_diagram` · `Mathematical_economics` · `Mathematical_finance` · `Mathematical_model_(disambiguation)` · [[Mathematical_optimization]] · `Mathematical_physics` · `Mathematical_psychology` · `Mathematical_sociology` · `Maxwell's_equations` · `Mechanics` · `Microscale_and_macroscale_models` · `Model` · `Molecular_model` · `Molecular_orbital` · `Mushroom` · `Nash_equilibrium` · `Natural_science` · `Neighbour-sensing_model` · [[Newton's_laws_of_motion]] · `Newton's_method` · `Nonlinear_system_identification` · `Nonparametric_statistics` · `Occam's_razor` · [[Operations_research]] · `Optimal_foraging_theory` · `Ordinal_utility` · `Overfitting` · `Paradigm_shift` · `Parameter` · `Pareto_efficiency` · `Particle_in_a_box` · [[Physics]] · `Plus_Magazine` · `Population_(biology)` · [[Probability]] · [[Quantum_mechanics]] · `Random_variable` · `Real_number` · `Regular_expression` · `Regular_language` · `Resilience_(mathematics)` · [[Schrödinger_equation]] · `Sensitivity_analysis` · `Set_(mathematics)` · `Simulation` · `Social_science` · `Solution_concept` · `Special_relativity` · `Speed_of_light` · `Spherical_cow` · `Stanislav_Andreski` · `State-transition_table` · `State_diagram` · `State_variable` · `Statistical_model` · `Surrogate_model` · [[System]] · [[System_identification]] · `The_World_in_the_Model:_How_Economists_Work_and_Think` · `Theory` · `Theory_of_relativity` · `Thermodynamic_cycle` · `Thomas_Kuhn` · `Vector_space` · [[Wayback_Machine]] · `White_box_(software_engineering)`
## From the Real GENERATIVE library
*Mathematical model — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (STEM and Music room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Blackbox3D-withGraphs.svg).*
> A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. ([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_model))
<!-- REAL-GENERATIVE-MEDIA:END -->
> p5.js MicroSim stub · part of Systems Engineering · [Wikipedia source](https://en.wikipedia.org/wiki/Mathematical_model)
> Relation: subfield of systems engineering.
## Concept summary
A mathematical model is an abstract description of a concrete [[System|system]] using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling.
## Build checklist
- [ ] Claim it: set `status: in-progress` + `lease` + `leased_at`
- [ ] Write the child page explaining the concept (tie it back to systems engineering)
- [ ] Finalize parameter ranges and defaults
- [ ] Implement the p5.js sketch (drawing + control regions)
- [ ] Add caption + the learning objective on the page
- [ ] Set `status: done`
## p5.js sketch
```javascript
// MicroSim: Mathematical model
let controls = {};
function setup() {
// createCanvas(...); create sliders for the parameters above.
}
function draw() {
// background(...); read controls; render state-machine; respond live.
}
```
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Back to Systems Engineering
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## Semiotic profile
> *The semiotic universals this article invokes, machine-derived from the crossref — **unverified** (born so). Populated 2026-07-06 for the Systems room.*
**Universals (4):** 🟡 system (7) · 🟡 sequence (3) · 🟢 state (1) · 🟢 state machine diagrams (1)
**Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal
<!-- SEMIOTIC-PROFILE:END -->
<!-- REAL-GENERATIVE-MEDIA:START -->
## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Mathematical_model) : [Wikitube](https://en.wikitube.io/wiki/Mathematical_model)
## Previous hub tags
Tree parents: [[Control_theory]] · [[Decision_theory]] · [[Dynamical_system]] · [[Game_theory]] · [[Operations_research]] · [[Reliability_engineering]] · [[System_dynamics]] · [[Systems_engineering]] · [[Systems_theory]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*